J. Korean Math. Soc. 2016; 53(6): 1331-1345
Online first article August 25, 2016 Printed November 1, 2016
https://doi.org/10.4134/JKMS.j150499
Copyright © The Korean Mathematical Society.
Dingli Hua and Yongdong Huang
Beifang University of Nationalities, Beifang University of Nationalities
A $K$-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator $K$ in Hilbert spaces. $K$-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a $K$-g-frame, which is different from a g-frame, is discussed. Several construction methods of $K$-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of $K$-g-frames are obtained.
Keywords: $K$-g-frame, frame, g-Bessel sequence, stability
MSC numbers: Primary 42C15, 42C40
2024; 61(2): 227-253
2022; 59(4): 733-756
2022; 59(2): 279-298
2021; 58(5): 1109-1129
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd